text{* The rewrites accumulated in @{text algebra_simps} deal with theclassical algebraic structures of groups, rings and family. They simplifyterms by multiplying everything out (in case of a ring) and bringing sums andproducts into a canonical form (by ordered rewriting). As a result it decidesgroup and ring equalities but also helps with inequalities.

Of course it also works for fields, but it knows nothing about multiplicativeinverses or division. This is catered for by @{text field_simps}. *}

text{* Lemmas @{text field_simps} multiply with denominators in (in)equationsif they can be proved to be non-zero (for equations) or positive/negative(for inequations). Can be too aggressive and is therefore separate from themore benign @{text algebra_simps}. *}